|
UWSpace >
University of Waterloo >
Electronic Theses and Dissertations (UW) >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10012/1180
|
| Title: | Two- and Three-Dimensional Coding Schemes for Wavelet and Fractal-Wavelet Image Compression |
| Authors: | Alexander, Simon |
| Keywords: | Mathematics
image compression
wavelets
fractal
arithmetic coding
hierarchical context model |
| Approved Date: | 2001 |
| Date Submitted: | 2001 |
| Abstract: | This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed: Iterated function systems (IFS) and wavelet-based approximations. IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle. Natural images under a wavelet basis have characteristic coefficient magnitude decays which may be used to aid approximation. The relationship between quantization, modelling, and encoding in a compression scheme is examined. Context based adaptive arithmetic coding is described. This encoding method is used in the coding schemes developed. A coder with explicit separation of the modelling and encoding roles is presented: an embedded wavelet bitplane coder based on hierarchical context in the wavelet coefficient trees. Fractal (spatial IFSM) and fractal-wavelet (coefficient tree), or IFSW, coders are discussed. A second coder is proposed, merging the IFSW approaches with the embedded bitplane coder. Performance of the coders, and applications to two- and three-dimensional images are discussed. Applications include two-dimensional still images in greyscale and colour, and three-dimensional streams (video). |
| Department: | Applied Mathematics |
| Degree: | Master of Mathematics |
| URI: | http://hdl.handle.net/10012/1180 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
|
This item is protected by original copyright
|
All items in UWSpace are protected by copyright, with all rights reserved.
|
